%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU688^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:32:59 AM UTC 2026
% Result : Theorem 206.98s 29.45s
% Output : Refutation 206.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of formulae : 157 ( 57 unt; 0 typ; 7 def)
% Number of atoms : 1901 ( 444 equ; 0 cnn)
% Maximal formula atoms : 11 ( 12 avg)
% Number of connectives : 3314 ( 86 ~; 277 |; 82 &;2610 @)
% ( 7 <=>; 143 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 45 usr; 19 con; 0-4 aty)
% ( 78 !!; 31 ??; 0 @@+; 0 @@-)
% Number of variables : 618 ( 22 sgn 280 !; 17 ?; 618 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_5,type,
kpair: $i > $i > $i ).
thf(func_def_6,type,
cartprod: $i > $i > $i ).
thf(func_def_7,type,
singleton: $i > $o ).
thf(func_def_9,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_10,type,
breln: $i > $i > $i > $o ).
thf(func_def_11,type,
func: $i > $i > $i > $o ).
thf(func_def_12,type,
funcSet: $i > $i > $i ).
thf(func_def_13,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_14,type,
infuncsetfunc: $o ).
thf(func_def_15,type,
funcGraphProp2: $o ).
thf(func_def_18,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_19,type,
vIMP: $o > $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vNOT: $o > $o ).
thf(func_def_35,type,
sK5: $i > $i > $i > $i ).
thf(func_def_36,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
sK6: $i > $i > $i > $i ).
thf(func_def_39,type,
sK8: $i > $i ).
thf(func_def_40,type,
sK9: $i > $i ).
thf(f1,axiom,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(f3,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f4,axiom,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(f5,axiom,
! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ( func @ X0 @ X1 @ X2 ) )
= infuncsetfunc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(f6,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( func @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(f7,conjecture,
( infuncsetfunc
=> ( funcGraphProp2
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(f8,negated_conjecture,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X2 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f9,plain,
~ ( infuncsetfunc
=> ( funcGraphProp2
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f10,plain,
~ ( ( infuncsetfunc = $true )
=> ( ( funcGraphProp2 = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ! [X4: $i] :
( ( ( in @ X4 @ X2 )
= $true )
=> ( ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X0 @ X2 ) )
=> ( func @ X0 @ X2 @ X1 ) )
= infuncsetfunc ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( func @ Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X2 @ X1 @ X0 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ( ^ [X0: $i,X1: $i > $o] :
( singleton
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) ) ) )
= ex1 ),
inference(rectify,[],[f2]) ).
thf(f16,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f18,plain,
( func
= ( ^ [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ex1 @ X1
@ ^ [X4: $i] : ( in @ ( kpair @ X3 @ X4 ) @ X2 ) ) )
& ( breln @ X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f19,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
( ( ^ [X0: $i] :
? [X1: $i] :
( ( in @ X1 @ X0 )
& ( X0
= ( setadjoin @ X1 @ emptyset ) ) ) )
= singleton ),
inference(rectify,[],[f1]) ).
thf(f21,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f20]) ).
thf(f22,plain,
( ? [X2: $i,X1: $i,X0: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
& ( ( in @ X4 @ X2 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true ) )
& ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f23,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( funcSet @ X1 @ X2 ) )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
= $true )
& ( ( in @ X4 @ X2 )
= $true ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( funcSet @ X2 @ X0 ) )
= $true )
& ? [X3: $i] :
( ? [X4: $i] :
( ( ( ap @ X2 @ X0 @ X1 @ X3 )
!= X4 )
& ( ( in @ ( kpair @ X3 @ X4 ) @ X1 )
= $true )
& ( ( in @ X4 @ X0 )
= $true ) )
& ( ( in @ X3 @ X2 )
= $true ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f25,plain,
( ( funcGraphProp2 = $true )
& ( infuncsetfunc = $true )
& ( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
= $true )
& ( ( ap @ sK2 @ sK0 @ sK1 @ sK3 )
!= sK4 )
& ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $true )
& ( ( in @ sK4 @ sK0 )
= $true )
& ( ( in @ sK3 @ sK2 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f24]) ).
thf(f26,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f27,plain,
( infuncsetfunc
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( func @ Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f28,plain,
( funcGraphProp2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( func @ Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f29,plain,
( singleton
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= Y0 )
& ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f30,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( singleton
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f31,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( breln @ Y0 @ Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ex1 @ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f32,plain,
( ( in @ sK3 @ sK2 )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f33,plain,
( ( in @ sK4 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f34,plain,
( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f35,plain,
( ( ap @ sK2 @ sK0 @ sK1 @ sK3 )
!= sK4 ),
inference(cnf_transformation,[],[f25]) ).
thf(f36,plain,
( ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) )
= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f37,plain,
infuncsetfunc = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f38,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[],[f25]) ).
thf(f41,plain,
( ex1
= ( ^ [Y0: $i,Y1: $i > $o] :
( ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= Y2 )
& ( in @ Y3 @ Y2 ) ) )
@ ( dsetconstr @ Y0
@ ^ [Y2: $i] : ( Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f30,f29]) ).
thf(f42,plain,
( func
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y0
@ Y1
@ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ^ [Y4: $i,Y5: $i > $o] :
( ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( ( setadjoin @ Y7 @ emptyset )
= Y6 )
& ( in @ Y7 @ Y6 ) ) )
@ ( dsetconstr @ Y4
@ ^ [Y6: $i] : ( Y5 @ Y6 ) ) )
@ Y1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f31,f26,f41]) ).
thf(f43,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y0
@ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f27,f37,f42]) ).
thf(f44,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f28,f38,f42]) ).
thf(f45,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y0
@ Y1
@ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y1 )
=> ( ( in @ ( kpair @ Y3 @ Y4 ) @ Y2 )
=> ( ( ap @ Y0 @ Y1 @ Y2 @ Y3 )
= Y4 ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ X1 @ Y0 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( subset @ Y1 @ ( cartprod @ X1 @ Y0 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) )
& ( in @ Y3
@ ( dsetconstr @ Y0
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y1 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y0 )
=> ( ( in @ ( kpair @ Y2 @ Y3 ) @ Y1 )
=> ( ( ap @ X1 @ Y0 @ Y1 @ Y2 )
= Y3 ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ X1 @ X2 @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( subset @ Y0 @ ( cartprod @ X1 @ X2 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) )
& ( in @ Y2
@ ( dsetconstr @ X2
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ Y0 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
=> ( ( in @ ( kpair @ Y1 @ Y2 ) @ Y0 )
=> ( ( ap @ X1 @ X2 @ Y0 @ Y1 )
= Y2 ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f48]) ).
thf(f50,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) ) ) )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ Y0 )
= Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f49]) ).
thf(f51,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ Y0 )
= Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ Y0 )
= Y1 ) ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ Y0 )
= Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X2 )
=> ( ( in @ ( kpair @ Y0 @ Y1 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ Y0 )
= Y1 ) ) ) ) )
@ X4 )
= $true )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X2
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X3 ) ) ) ) ) )
@ ( sK5 @ X3 @ X1 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ( in @ X4 @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) ) ) )
= $true )
| ( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) ) )
= $true )
| ( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f55]) ).
thf(f57,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) )
@ X5 )
= $true )
| ( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) ) ) ) )
= $false )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) ) ) ) )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) )
@ X5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) )
@ X5 )
= $true )
| ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f57]) ).
thf(f60,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f61,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) )
= $true )
| ( ( in @ X5 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f60]) ).
thf(f62,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( in @ X5 @ X2 )
= $false )
| ( ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 )
= $true )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( in @ ( sK5 @ X3 @ X1 @ X2 ) @ X1 )
= $true )
| ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $false )
| ( ( in @ X5 @ X2 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ X4 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X2
@ ^ [Y1: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y1 ) @ X3 ) ) ) )
@ X6 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X2 )
=> ( ( in @ ( kpair @ X4 @ Y0 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= Y0 ) ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f58]) ).
thf(f65,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( $false
= ( ( ( setadjoin @ X6 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
& ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ X2 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) ) )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( $false
= ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( $false
= ( ( setadjoin @ X6 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ X5 @ X2 )
= $false )
| ( ( in @ X4 @ X1 )
= $false )
| ( $false
= ( ( setadjoin @ X6 @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
| ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
=> ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 ) )
= $true )
| ( $false
= ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) )
!= ( setadjoin @ X6 @ emptyset ) )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ X5 @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f67]) ).
thf(f69,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X2 )
= $false )
| ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) )
!= ( setadjoin @ X6 @ emptyset ) )
| ( ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 )
= $true )
| ( ( in @ X4 @ X1 )
= $false )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $false )
| ( $false
= ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) )
!= ( setadjoin @ X6 @ emptyset ) )
| ( ( subset @ X3 @ ( cartprod @ X1 @ X2 ) )
= $false )
| ( ( ap @ X1 @ X2 @ X3 @ X4 )
= X5 )
| ( ( in @ X5 @ X2 )
= $false )
| ( ( in @ X4 @ X1 )
= $false )
| ( $false
= ( in @ X6
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X3 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X3 )
= $false ) ),
inference(equality_proxy_clausification,[],[f69]) ).
thf(f71,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( funcSet @ Y2 @ Y0 ) )
=> ( ^ [Y3: $i,Y4: $i,Y5: $i] :
( ( ^ [Y6: $i,Y7: $i,Y8: $i] : ( subset @ Y8 @ ( cartprod @ Y6 @ Y7 ) )
@ Y3
@ Y4
@ Y5 )
& ( !! @ $i
@ ^ [Y6: $i] :
( ( in @ Y6 @ Y3 )
=> ( ^ [Y7: $i,Y8: $i > $o] :
( ^ [Y9: $i] :
( ?? @ $i
@ ^ [Y10: $i] :
( ( ( setadjoin @ Y10 @ emptyset )
= Y9 )
& ( in @ Y10 @ Y9 ) ) )
@ ( dsetconstr @ Y7
@ ^ [Y9: $i] : ( Y8 @ Y9 ) ) )
@ Y4
@ ^ [Y7: $i] : ( in @ ( kpair @ Y6 @ Y7 ) @ Y5 ) ) ) ) )
@ Y2
@ Y0
@ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f43]) ).
thf(f72,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ Y1 @ X1 ) )
=> ( ( subset @ Y0 @ ( cartprod @ Y1 @ X1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) )
& ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f71]) ).
thf(f73,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( funcSet @ Y1 @ X1 ) )
=> ( ( subset @ Y0 @ ( cartprod @ Y1 @ X1 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ Y3 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) )
& ( in @ Y3
@ ( dsetconstr @ X1
@ ^ [Y4: $i] : ( in @ ( kpair @ Y2 @ Y4 ) @ Y0 ) ) ) ) ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f72]) ).
thf(f74,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ Y0 @ X1 ) )
=> ( ( subset @ X2 @ ( cartprod @ Y0 @ X1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) )
& ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f73]) ).
thf(f75,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( funcSet @ Y0 @ X1 ) )
=> ( ( subset @ X2 @ ( cartprod @ Y0 @ X1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ Y2 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) )
& ( in @ Y2
@ ( dsetconstr @ X1
@ ^ [Y3: $i] : ( in @ ( kpair @ Y1 @ Y3 ) @ X2 ) ) ) ) ) ) ) ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
=> ( ( subset @ X2 @ ( cartprod @ X3 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false )
| ( ( ( subset @ X2 @ ( cartprod @ X3 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) ) ) ) ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( subset @ X2 @ ( cartprod @ X3 @ X1 ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f80,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ X3 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ Y1 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) )
& ( in @ Y1
@ ( dsetconstr @ X1
@ ^ [Y2: $i] : ( in @ ( kpair @ Y0 @ Y2 ) @ X2 ) ) ) ) ) )
@ X4 )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f78]) ).
thf(f81,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false )
| ( ( ( in @ X4 @ X3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X3 )
= $false )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) ) ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( setadjoin @ Y0 @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) )
& ( in @ Y0
@ ( dsetconstr @ X1
@ ^ [Y1: $i] : ( in @ ( kpair @ X4 @ Y1 ) @ X2 ) ) ) )
@ ( sK6 @ X2 @ X1 @ X4 ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ( ( setadjoin @ ( sK6 @ X2 @ X1 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
& ( in @ ( sK6 @ X2 @ X1 @ X4 )
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false )
| ( ( in @ X4 @ X3 )
= $false ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X4 @ X3 )
= $false )
| ( ( in @ ( sK6 @ X2 @ X1 @ X4 )
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
= $true )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false )
| ( ( ( setadjoin @ ( sK6 @ X2 @ X1 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
= $true )
| ( ( in @ X4 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f87,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( sK6 @ X2 @ X1 @ X4 ) @ emptyset )
= ( dsetconstr @ X1
@ ^ [Y0: $i] : ( in @ ( kpair @ X4 @ Y0 ) @ X2 ) ) )
| ( ( in @ X2 @ ( funcSet @ X3 @ X1 ) )
= $false )
| ( ( in @ X4 @ X3 )
= $false ) ),
inference(equality_proxy_clausification,[],[f86]) ).
thf(f110,definition,
( spl7_1
<=> ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f111,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
!= $false )
| spl7_1 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f112,plain,
( ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f118,definition,
( spl7_3
<=> ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( sK4 != X0 )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f119,plain,
( ! [X0: $i] :
( ( sK4 != X0 )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( in @ X3 @ ( funcSet @ X1 @ X4 ) ) )
| ( $false = $true )
| ( $false
= ( in @ X6 @ X2 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X5 )
= X6 )
| ( ( setadjoin @ ( sK6 @ X3 @ X4 @ ( sK5 @ X0 @ X1 @ X2 ) ) @ emptyset )
= ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
| ( $false
= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) )
| ( $false
= ( in @ X5 @ X1 ) )
| ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(constrained_superposition,[],[f87,f63]) ).
thf(f136,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( in @ X0 @ ( funcSet @ X6 @ X1 ) )
= $false )
| ( ( in @ X2 @ X6 )
= $false )
| ( ( in @ ( sK6 @ X3 @ X1 @ X4 ) @ ( setadjoin @ ( sK6 @ X0 @ X1 @ X2 ) @ emptyset ) )
= $true )
| ( $false
= ( in @ X4 @ X5 ) )
| ( ( in @ X3 @ ( funcSet @ X5 @ X1 ) )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : X3 ) )
| ( ( ^ [Y0: $i] : X4 )
!= ( ^ [Y0: $i] : X2 ) ) ),
inference(constrained_superposition,[],[f85,f87]) ).
thf(f144,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( setadjoin @ ( sK6 @ X3 @ X4 @ ( sK5 @ X0 @ X1 @ X2 ) ) @ emptyset )
= ( dsetconstr @ X4
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ X0 @ X1 @ X2 ) @ Y0 ) @ X3 ) ) )
| ( ( ap @ X1 @ X2 @ X0 @ X5 )
= X6 )
| ( $false
= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) )
| ( $false
= ( in @ X6 @ X2 ) )
| ( $false
= ( in @ X5 @ X1 ) )
| ( $false
= ( in @ X3 @ ( funcSet @ X1 @ X4 ) ) )
| ( $false
= ( subset @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ),
inference(trivial_inequality_removal,[],[f132]) ).
thf(f312,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $false )
| ( ( in @ sK4 @ sK0 )
= $false )
| ~ spl7_3 ),
inference(equality_resolution,[],[f119]) ).
thf(f313,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $false )
| ( $false = $true )
| ~ spl7_3 ),
inference(forward_demodulation,[],[f312,f33]) ).
thf(f314,plain,
( ( ( in @ ( kpair @ sK3 @ sK4 ) @ sK1 )
= $false )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
( ( $false = $true )
| ~ spl7_3 ),
inference(constrained_superposition,[],[f314,f34]) ).
thf(f321,plain,
( $false
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f322,plain,
~ spl7_3,
inference(avatar_contradiction_clause,[],[f321]) ).
thf(f1147,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false )
| ( ( in @ sK3 @ sK2 )
= $false )
| ( ( setadjoin @ ( sK6 @ X1 @ X2 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ Y0 ) @ X1 ) ) )
| ( ( in @ X1 @ ( funcSet @ sK2 @ X2 ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( sK4 != X0 ) ),
inference(constrained_superposition,[],[f35,f144]) ).
thf(f1186,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( ( in @ X1 @ ( funcSet @ sK2 @ X2 ) )
= $false )
| ( sK4 != X0 )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( setadjoin @ ( sK6 @ X1 @ X2 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ Y0 ) @ X1 ) ) )
| ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false ) ),
inference(forward_demodulation,[],[f1147,f32]) ).
thf(f1187,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( setadjoin @ ( sK6 @ X1 @ X2 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ Y0 ) @ X1 ) ) )
| ( ( in @ X1 @ ( funcSet @ sK2 @ X2 ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( sK4 != X0 )
| ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f1186]) ).
thf(f1189,definition,
( spl7_5
<=> ! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( sK6 @ X1 @ X2 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ Y0 ) @ X1 ) ) )
| ( ( in @ X1 @ ( funcSet @ sK2 @ X2 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f1190,plain,
( ! [X2: $i,X1: $i] :
( ( ( setadjoin @ ( sK6 @ X1 @ X2 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
= ( dsetconstr @ X2
@ ^ [Y0: $i] : ( in @ ( kpair @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ Y0 ) @ X1 ) ) )
| ( ( in @ X1 @ ( funcSet @ sK2 @ X2 ) )
= $false ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f1189]) ).
thf(f1191,plain,
( spl7_1
| spl7_3
| spl7_5 ),
inference(avatar_split_clause,[],[f1187,f1189,f118,f110]) ).
thf(f1192,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f112,f79]) ).
thf(f1196,plain,
( ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f1192]) ).
thf(f1198,plain,
( ( $false = $true )
| ~ spl7_1 ),
inference(constrained_superposition,[],[f1196,f36]) ).
thf(f1204,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f1198]) ).
thf(f1205,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f1204]) ).
thf(f2443,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X1 ) )
| ( ( in @ X3 @ X1 )
= $false )
| ( ( in @ X2 @ ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
!= ( setadjoin @ X2 @ emptyset ) )
| ( ( in @ X0 @ ( funcSet @ sK2 @ sK0 ) )
= $false )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $false )
| ( $false
= ( in @ X4 @ sK0 ) )
| ( ( ap @ X1 @ sK0 @ sK1 @ X3 )
= X4 )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X1 @ sK0 ) ) ) )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f70,f1190]) ).
thf(f2450,definition,
( spl7_8
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X1 ) )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X1 @ sK0 ) ) )
| ( ( ap @ X1 @ sK0 @ sK1 @ X3 )
= X4 )
| ( $false
= ( in @ X4 @ sK0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $false )
| ( ( in @ X3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f2451,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] : sK2 )
!= ( ^ [Y0: $i] : X1 ) )
| ( $false
= ( in @ X4 @ sK0 ) )
| ( ( in @ ( kpair @ X3 @ X4 ) @ sK1 )
= $false )
| ( $false
= ( subset @ sK1 @ ( cartprod @ X1 @ sK0 ) ) )
| ( ( ap @ X1 @ sK0 @ sK1 @ X3 )
= X4 )
| ( ( in @ X3 @ X1 )
= $false ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f2450]) ).
thf(f2453,definition,
( spl7_9
<=> ! [X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( in @ X0 @ ( funcSet @ sK2 @ sK0 ) )
= $false )
| ( ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
!= ( setadjoin @ X2 @ emptyset ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f2454,plain,
( ! [X2: $i,X0: $i] :
( ( ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset )
!= ( setadjoin @ X2 @ emptyset ) )
| ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( in @ X2 @ ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( ( in @ X0 @ ( funcSet @ sK2 @ sK0 ) )
= $false ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f2453]) ).
thf(f2455,plain,
( spl7_8
| spl7_9
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f2443,f1189,f2453,f2450]) ).
thf(f8038,definition,
( spl7_11
<=> ! [X4: $i,X5: $i] :
( ( ( in @ X5 @ sK0 )
= $false )
| ( ( in @ X4 @ sK2 )
= $false )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X4 )
= X5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f8039,plain,
( ! [X4: $i,X5: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ X4 )
= X5 )
| ( $false
= ( in @ ( kpair @ X4 @ X5 ) @ sK1 ) )
| ( ( in @ X5 @ sK0 )
= $false )
| ( ( in @ X4 @ sK2 )
= $false ) )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f8038]) ).
thf(f13553,plain,
( ! [X0: $i] :
( ( ( ^ [Y0: $i] : X0 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( in @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ ( setadjoin @ ( sK6 @ X0 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( ( in @ X0 @ ( funcSet @ sK2 @ sK0 ) )
= $false ) )
| ~ spl7_9 ),
inference(equality_resolution,[],[f2454]) ).
thf(f20633,plain,
( ( ( in @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ ( setadjoin @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
| ~ spl7_9 ),
inference(equality_resolution,[],[f13553]) ).
thf(f20635,plain,
( ( ( in @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ ( setadjoin @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ( $false = $true )
| ~ spl7_9 ),
inference(forward_demodulation,[],[f20633,f36]) ).
thf(f20636,plain,
( ( ( in @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ ( setadjoin @ ( sK6 @ sK1 @ sK0 @ ( sK5 @ sK1 @ sK2 @ sK0 ) ) @ emptyset ) )
= $false )
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f20635]) ).
thf(f21897,plain,
( ! [X0: $i,X1: $i] :
( ( ( ^ [Y0: $i] : sK1 )
!= ( ^ [Y0: $i] : sK1 ) )
| ( ( in @ sK1 @ ( funcSet @ X1 @ sK0 ) )
= $false )
| ( $false = $true )
| ( $false
= ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X0 ) )
| ( ( ^ [Y0: $i] : ( sK5 @ sK1 @ sK2 @ sK0 ) )
!= ( ^ [Y0: $i] : ( sK5 @ sK1 @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ sK1 @ ( funcSet @ X0 @ sK0 ) ) )
| ( ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X1 )
= $false ) )
| ~ spl7_9 ),
inference(constrained_superposition,[],[f20636,f136]) ).
thf(f21917,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X0 ) )
| ( ( in @ sK1 @ ( funcSet @ X1 @ sK0 ) )
= $false )
| ( $false
= ( in @ sK1 @ ( funcSet @ X0 @ sK0 ) ) )
| ( ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X1 )
= $false ) )
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f21897]) ).
thf(f21920,definition,
( spl7_21
<=> ! [X0: $i] :
( ( $false
= ( in @ sK1 @ ( funcSet @ X0 @ sK0 ) ) )
| ( $false
= ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_21])],[avatar_definition]) ).
thf(f21921,plain,
( ! [X0: $i] :
( ( $false
= ( in @ ( sK5 @ sK1 @ sK2 @ sK0 ) @ X0 ) )
| ( $false
= ( in @ sK1 @ ( funcSet @ X0 @ sK0 ) ) ) )
| ~ spl7_21 ),
inference(avatar_component_clause,[],[f21920]) ).
thf(f21943,plain,
( ! [X0: $i,X1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ X1 )
= X0 )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK1 )
= $false )
| ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( $false
= ( in @ X1 @ sK2 ) ) )
| ~ spl7_8 ),
inference(equality_resolution,[],[f2451]) ).
thf(f21945,plain,
( ! [X0: $i,X1: $i] :
( ( ( ap @ sK2 @ sK0 @ sK1 @ X1 )
= X0 )
| ( ( in @ ( kpair @ X1 @ X0 ) @ sK1 )
= $false )
| ( ( in @ X0 @ sK0 )
= $false )
| ( $false
= ( in @ X1 @ sK2 ) ) )
| spl7_1
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f21943,f111]) ).
thf(f21946,plain,
( spl7_11
| spl7_1
| ~ spl7_8 ),
inference(avatar_split_clause,[],[f21945,f2450,f110,f8038]) ).
thf(f21994,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ sK3 @ sK2 )
= $false )
| ( sK4 != X0 )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false ) )
| ~ spl7_11 ),
inference(constrained_superposition,[],[f35,f8039]) ).
thf(f22055,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( $false = $true )
| ( sK4 != X0 ) )
| ~ spl7_11 ),
inference(forward_demodulation,[],[f21994,f32]) ).
thf(f22056,plain,
( ! [X0: $i] :
( ( ( in @ X0 @ sK0 )
= $false )
| ( ( in @ ( kpair @ sK3 @ X0 ) @ sK1 )
= $false )
| ( sK4 != X0 ) )
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f22055]) ).
thf(f22071,plain,
( spl7_3
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f22056,f8038,f118]) ).
thf(f22103,plain,
( spl7_21
| spl7_21
| ~ spl7_9 ),
inference(avatar_split_clause,[],[f21917,f2453,f21920,f21920]) ).
thf(f25385,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ X0 @ sK2 ) )
| ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK1 ) )
| ( $false = $true )
| ( ( in @ X1 @ sK0 )
= $false )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X0 )
= X1 )
| ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) ) )
| ~ spl7_21 ),
inference(constrained_superposition,[],[f21921,f63]) ).
thf(f25393,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ sK1 @ ( cartprod @ sK2 @ sK0 ) )
= $false )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X0 )
= X1 )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK1 ) )
| ( ( in @ X1 @ sK0 )
= $false ) )
| ~ spl7_21 ),
inference(trivial_inequality_removal,[],[f25385]) ).
thf(f25399,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK1 ) )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X0 )
= X1 )
| ( ( in @ X1 @ sK0 )
= $false )
| ( $false
= ( in @ sK1 @ ( funcSet @ sK2 @ sK0 ) ) )
| ( $false
= ( in @ X0 @ sK2 ) ) )
| spl7_1
| ~ spl7_21 ),
inference(forward_subsumption_resolution,[],[f25393,f111]) ).
thf(f25403,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK1 ) )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( ( in @ X1 @ sK0 )
= $false )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X0 )
= X1 ) )
| spl7_1
| ~ spl7_21 ),
inference(forward_demodulation,[],[f25399,f36]) ).
thf(f25404,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ sK0 )
= $false )
| ( $false
= ( in @ X0 @ sK2 ) )
| ( ( ap @ sK2 @ sK0 @ sK1 @ X0 )
= X1 )
| ( $false
= ( in @ ( kpair @ X0 @ X1 ) @ sK1 ) ) )
| spl7_1
| ~ spl7_21 ),
inference(trivial_inequality_removal,[],[f25403]) ).
thf(f25411,plain,
( spl7_11
| spl7_1
| ~ spl7_21 ),
inference(avatar_split_clause,[],[f25404,f21920,f110,f8038]) ).
cnf(s4,plain,
~ spl7_3,
inference(sat_conversion,[],[f322]) ).
cnf(s5,plain,
( spl7_1
| spl7_3
| spl7_5 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s7,plain,
~ spl7_1,
inference(sat_conversion,[],[f1205]) ).
cnf(s10,plain,
( ~ spl7_5
| spl7_8
| spl7_9 ),
inference(sat_conversion,[],[f2455]) ).
cnf(s36,plain,
( spl7_1
| ~ spl7_8
| spl7_11 ),
inference(sat_conversion,[],[f21946]) ).
cnf(s50,plain,
( spl7_3
| ~ spl7_11 ),
inference(sat_conversion,[],[f22071]) ).
cnf(s77,plain,
( spl7_21
| ~ spl7_9
| spl7_21 ),
inference(sat_conversion,[],[f22103]) ).
cnf(s78,plain,
( ~ spl7_9
| spl7_21 ),
inference(rat,[],[s77]) ).
cnf(s83,plain,
( spl7_1
| spl7_11
| ~ spl7_21 ),
inference(sat_conversion,[],[f25411]) ).
cnf(s87,plain,
( spl7_3
| spl7_5 ),
inference(rat,[],[s5,s7]) ).
cnf(s89,plain,
~ spl7_11,
inference(rat,[],[s50,s4]) ).
cnf(s100,plain,
spl7_5,
inference(rat,[],[s87,s4]) ).
cnf(s101,plain,
~ spl7_21,
inference(rat,[],[s83,s7,s89]) ).
cnf(s102,plain,
~ spl7_8,
inference(rat,[],[s36,s7,s89]) ).
cnf(s104,plain,
~ spl7_9,
inference(rat,[],[s78,s101]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s10,s100,s104,s102]) ).
thf(f25413,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU688^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 % Computer : n001.cluster.edu
% 0.10/0.25 % Model : x86_64 x86_64
% 0.10/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.25 % Memory : 8046.5625MB
% 0.10/0.25 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 14:15:06 UTC 2026
% 0.10/0.26 % CPUTime :
% 0.10/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.24/0.31 Running first-order model finding
% 0.24/0.31 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.88/1.49 % (1306520)Will run a generic schedule for satisfiability detection.
% 6.88/1.49 % (1306526)% WARNING: option uhcvi not known.
% 6.88/1.49 % (1306526)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3357294329:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.88/1.49 % (1306526)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.88/1.49 % (1306526)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.88/1.49 % (1306525)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1293807610_2999 on theBenchmark for (2999ds/0Mi)
% 6.88/1.49 % Exception at run slice level
% 6.88/1.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.88/1.49 % (1306528)dis+10_1_sil=32000:sp=arity:random_seed=230015768:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.88/1.49 % (1306529)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2794992757:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.88/1.49 % (1306530)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=25234922:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.88/1.49 % (1306531)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2294735432:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.88/1.49 % (1306527)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1657457479:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.88/1.49 % (1306529)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.88/1.49 % (1306534)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=294229602:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.88/1.49 % Exception at run slice level
% 6.88/1.49 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.88/1.49 % (1306541)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=504994318:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.88/1.49 % (1306528)Instruction limit reached!
% 6.88/1.49 % (1306528)------------------------------
% 6.88/1.49 % (1306528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1306528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1306528)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1306528)Termination reason: Instruction limit
% 6.88/1.49 % (1306528)Termination phase: Saturation
% 6.88/1.49 % (1306528)Time elapsed: 0.082 s
% 6.88/1.49 % (1306528)Peak memory usage: 12 MB
% 6.88/1.49 % (1306528)Instructions burned: 103 (million)
% 6.88/1.49 % (1306529)Instruction limit reached!
% 6.88/1.49 % (1306529)------------------------------
% 6.88/1.49 % (1306529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1306529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1306529)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1306529)Termination reason: Instruction limit
% 6.88/1.49 % (1306529)Termination phase: Saturation
% 6.88/1.49 % (1306529)Time elapsed: 0.095 s
% 6.88/1.49 % (1306529)Peak memory usage: 12 MB
% 6.88/1.49 % (1306529)Instructions burned: 116 (million)
% 6.88/1.49 % (1306530)Instruction limit reached!
% 6.88/1.49 % (1306530)------------------------------
% 6.88/1.49 % (1306530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.88/1.49 % (1306530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.88/1.49 % (1306530)CaDiCaL version: 2.1.3
% 6.88/1.49 % (1306530)Termination reason: Instruction limit
% 6.88/1.49 % (1306530)Termination phase: Saturation
% 6.88/1.49 % (1306530)Time elapsed: 0.108 s
% 6.88/1.49 % (1306530)Peak memory usage: 12 MB
% 6.88/1.49 % (1306530)Instructions burned: 131 (million)
% 6.88/1.49 % (1306543)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=121613938:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 6.88/1.49 % (1306543)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.88/1.49 % (1306543)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.88/1.49 % (1306544)ott-21_1_sil=16000:fs=off:random_seed=3174499607:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 6.88/1.49 % (1306531)Instruction limit reached!
% 27.49/4.25 % (1306531)------------------------------
% 27.49/4.25 % (1306531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.49/4.25 % (1306531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.49/4.25 % (1306531)CaDiCaL version: 2.1.3
% 27.49/4.25 % (1306531)Termination reason: Instruction limit
% 27.49/4.25 % (1306531)Termination phase: Saturation
% 27.49/4.25 % (1306531)Time elapsed: 0.132 s
% 27.49/4.25 % (1306531)Peak memory usage: 12 MB
% 27.49/4.25 % (1306531)Instructions burned: 160 (million)
% 27.49/4.25 % (1306545)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2388978095:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 27.49/4.25 % (1306541)Instruction limit reached!
% 27.49/4.25 % (1306541)------------------------------
% 27.49/4.25 % (1306541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.49/4.25 % (1306541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.49/4.25 % (1306541)CaDiCaL version: 2.1.3
% 27.49/4.25 % (1306541)Termination reason: Instruction limit
% 27.49/4.25 % (1306541)Termination phase: Saturation
% 27.49/4.25 % (1306541)Time elapsed: 0.097 s
% 27.49/4.25 % (1306541)Peak memory usage: 13 MB
% 27.49/4.25 % (1306541)Instructions burned: 131 (million)
% 27.49/4.25 % (1306548)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1676378544:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 27.49/4.25 % Exception at run slice level
% 27.49/4.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.49/4.25 % (1306551)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1742093682:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 27.49/4.25 % (1306552)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1513579798:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 27.49/4.25 % Exception at run slice level
% 27.49/4.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.49/4.25 % (1306555)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3318202464:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 27.49/4.25 % (1306555)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 27.49/4.25 % (1306544)Instruction limit reached!
% 27.49/4.25 % (1306544)------------------------------
% 27.49/4.25 % (1306544)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.49/4.25 % (1306544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.49/4.25 % (1306544)CaDiCaL version: 2.1.3
% 27.49/4.25 % (1306544)Termination reason: Instruction limit
% 27.49/4.25 % (1306544)Termination phase: Saturation
% 27.49/4.25 % (1306544)Time elapsed: 0.145 s
% 27.49/4.25 % (1306544)Peak memory usage: 12 MB
% 27.49/4.25 % (1306544)Instructions burned: 181 (million)
% 27.49/4.25 % (1306557)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=716530391:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 27.49/4.25 % (1306557)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 27.49/4.25 % (1306545)Instruction limit reached!
% 27.49/4.25 % (1306545)------------------------------
% 27.49/4.25 % (1306545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 27.49/4.25 % (1306545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 27.49/4.25 % (1306545)CaDiCaL version: 2.1.3
% 27.49/4.25 % (1306545)Termination reason: Instruction limit
% 27.49/4.25 % (1306545)Termination phase: Saturation
% 27.49/4.25 % (1306545)Time elapsed: 0.415 s
% 27.49/4.25 % (1306545)Peak memory usage: 13 MB
% 27.49/4.25 % (1306545)Instructions burned: 478 (million)
% 27.49/4.25 % (1306561)fmb+10_1_sil=64000:random_seed=151285339:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 27.49/4.25 % (1306561)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 27.49/4.25 % Exception at run slice level
% 27.49/4.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 27.49/4.25 % (1306563)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2113753829:i=9515:nm=5_2993 on theBenchmark for (2993ds/9515Mi)
% 27.49/4.25 % Exception at run slice level
% 27.49/4.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.20/8.53 % (1306565)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=960573892:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 58.20/8.53 % Exception at run slice level
% 58.20/8.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.20/8.53 % (1306543)Instruction limit reached!
% 58.20/8.53 % (1306543)------------------------------
% 58.20/8.53 % (1306543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.20/8.53 % (1306543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.20/8.53 % (1306543)CaDiCaL version: 2.1.3
% 58.20/8.53 % (1306543)Termination reason: Instruction limit
% 58.20/8.53 % (1306543)Termination phase: Saturation
% 58.20/8.53 % (1306543)Time elapsed: 0.552 s
% 58.20/8.53 % (1306543)Peak memory usage: 14 MB
% 58.20/8.53 % (1306543)Instructions burned: 685 (million)
% 58.20/8.53 % (1306567)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=4037374678:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 58.20/8.53 % (1306567)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 58.20/8.53 % (1306568)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=2714788596:i=1472:ins=7:fdi=8:gsp=on_2992 on theBenchmark for (2992ds/1472Mi)
% 58.20/8.53 % (1306568)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 58.20/8.53 % (1306568)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 58.20/8.53 % (1306555)Instruction limit reached!
% 58.20/8.53 % (1306555)------------------------------
% 58.20/8.53 % (1306555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.20/8.53 % (1306555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.20/8.53 % (1306555)CaDiCaL version: 2.1.3
% 58.20/8.53 % (1306555)Termination reason: Instruction limit
% 58.20/8.53 % (1306555)Termination phase: Saturation
% 58.20/8.53 % (1306555)Time elapsed: 0.555 s
% 58.20/8.53 % (1306555)Peak memory usage: 15 MB
% 58.20/8.53 % (1306555)Instructions burned: 692 (million)
% 58.20/8.53 % (1306571)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=776318973:i=6324_2991 on theBenchmark for (2991ds/6324Mi)
% 58.20/8.53 % Exception at run slice level
% 58.20/8.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.20/8.53 % (1306573)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=1135777219:fmbsr=2.30978:i=2174_2991 on theBenchmark for (2991ds/2174Mi)
% 58.20/8.53 % Exception at run slice level
% 58.20/8.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 58.20/8.53 % (1306575)ott-2_1_sil=16000:newcnf=on:random_seed=4181479485:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 58.20/8.53 % (1306575)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 58.20/8.53 % (1306557)Instruction limit reached!
% 58.20/8.53 % (1306557)------------------------------
% 58.20/8.53 % (1306557)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.20/8.53 % (1306557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.20/8.53 % (1306557)CaDiCaL version: 2.1.3
% 58.20/8.53 % (1306557)Termination reason: Instruction limit
% 58.20/8.53 % (1306557)Termination phase: Saturation
% 58.20/8.53 % (1306557)Time elapsed: 0.749 s
% 58.20/8.53 % (1306557)Peak memory usage: 14 MB
% 58.20/8.53 % (1306557)Instructions burned: 880 (million)
% 58.20/8.53 % (1306580)ott+10_1_sil=32000:tgt=ground:random_seed=1627367370:i=5114:av=off_2989 on theBenchmark for (2989ds/5114Mi)
% 58.20/8.53 % (1306551)Instruction limit reached!
% 58.20/8.53 % (1306551)------------------------------
% 58.20/8.53 % (1306551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 58.20/8.53 % (1306551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 58.20/8.53 % (1306551)CaDiCaL version: 2.1.3
% 58.20/8.53 % (1306551)Termination reason: Instruction limit
% 58.20/8.53 % (1306551)Termination phase: Saturation
% 58.20/8.53 % (1306551)Time elapsed: 0.937 s
% 58.20/8.53 % (1306551)Peak memory usage: 16 MB
% 58.20/8.53 % (1306551)Instructions burned: 1179 (million)
% 58.20/8.53 % (1306583)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2456126232:i=54282_2988 on theBenchmark for (2988ds/54282Mi)
% 58.20/8.53 % Exception at run slice level
% 58.20/8.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 152.48/21.90 % (1306585)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3713901025:i=3512:aac=none_2988 on theBenchmark for (2988ds/3512Mi)
% 152.48/21.90 % (1306585)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 152.48/21.90 % (1306575)Instruction limit reached!
% 152.48/21.90 % (1306575)------------------------------
% 152.48/21.90 % (1306575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 152.48/21.90 % (1306575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 152.48/21.90 % (1306575)CaDiCaL version: 2.1.3
% 152.48/21.90 % (1306575)Termination reason: Instruction limit
% 152.48/21.90 % (1306575)Termination phase: Saturation
% 152.48/21.90 % (1306575)Time elapsed: 0.684 s
% 152.48/21.90 % (1306575)Peak memory usage: 14 MB
% 152.48/21.90 % (1306575)Instructions burned: 869 (million)
% 152.48/21.90 % (1306595)dis+21_1_sil=32000:sas=cadical:random_seed=3334528340:i=3773:amm=off_2984 on theBenchmark for (2984ds/3773Mi)
% 152.48/21.90 % (1306568)Instruction limit reached!
% 152.48/21.90 % (1306568)------------------------------
% 152.48/21.90 % (1306568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 152.48/21.90 % (1306568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 152.48/21.90 % (1306568)CaDiCaL version: 2.1.3
% 152.48/21.90 % (1306568)Termination reason: Instruction limit
% 152.48/21.90 % (1306568)Termination phase: Saturation
% 152.48/21.90 % (1306568)Time elapsed: 1.229 s
% 152.48/21.90 % (1306568)Peak memory usage: 14 MB
% 152.48/21.90 % (1306568)Instructions burned: 1473 (million)
% 152.48/21.90 % (1306599)ott+11_1_sil=16000:gs=on:random_seed=4220496674:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2980 on theBenchmark for (2980ds/2251Mi)
% 152.48/21.90 % (1306599)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 152.48/21.90 % (1306580)Instruction limit reached!
% 152.48/21.90 % (1306580)------------------------------
% 152.48/21.90 % (1306580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 152.48/21.90 % (1306580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 152.48/21.90 % (1306580)CaDiCaL version: 2.1.3
% 152.48/21.90 % (1306580)Termination reason: Instruction limit
% 152.48/21.90 % (1306580)Termination phase: Saturation
% 152.48/21.90 % (1306580)Time elapsed: 1.901 s
% 152.48/21.90 % (1306580)Peak memory usage: 28 MB
% 152.48/21.90 % (1306580)Instructions burned: 5116 (million)
% 152.48/21.90 % (1306609)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=87268822:fmbsr=1.6:i=67534_2970 on theBenchmark for (2970ds/67534Mi)
% 152.48/21.90 % Exception at run slice level
% 152.48/21.90 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 152.48/21.90 % (1306611)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=1955789411:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2969 on theBenchmark for (2969ds/4591Mi)
% 152.48/21.90 % (1306599)Instruction limit reached!
% 152.48/21.90 % (1306599)------------------------------
% 152.48/21.90 % (1306599)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 152.48/21.90 % (1306599)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 152.48/21.90 % (1306599)CaDiCaL version: 2.1.3
% 152.48/21.90 % (1306599)Termination reason: Instruction limit
% 152.48/21.90 % (1306599)Termination phase: Saturation
% 152.48/21.90 % (1306599)Time elapsed: 1.686 s
% 152.48/21.90 % (1306599)Peak memory usage: 17 MB
% 152.48/21.90 % (1306599)Instructions burned: 2251 (million)
% 152.48/21.90 % (1306613)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=131936483:i=29340_2963 on theBenchmark for (2963ds/29340Mi)
% 152.48/21.90 % (1306585)Instruction limit reached!
% 152.48/21.90 % (1306585)------------------------------
% 152.48/21.90 % (1306585)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 152.48/21.90 % (1306585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 152.48/21.90 % (1306585)CaDiCaL version: 2.1.3
% 152.48/21.90 % (1306585)Termination reason: Instruction limit
% 152.48/21.90 % (1306585)Termination phase: Saturation
% 152.48/21.90 % (1306585)Time elapsed: 2.692 s
% 152.48/21.90 % (1306585)Peak memory usage: 17 MB
% 152.48/21.90 % (1306585)Instructions burned: 3512 (million)
% 152.48/21.90 % (1306618)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=2228261694:i=5211_2961 on theBenchmark for (2961ds/5211Mi)
% 206.98/29.45 % (1306595)Instruction limit reached!
% 206.98/29.45 % (1306595)------------------------------
% 206.98/29.45 % (1306595)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306595)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306595)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306595)Termination reason: Instruction limit
% 206.98/29.45 % (1306595)Termination phase: Saturation
% 206.98/29.45 % (1306595)Time elapsed: 2.841 s
% 206.98/29.45 % (1306595)Peak memory usage: 18 MB
% 206.98/29.45 % (1306595)Instructions burned: 3773 (million)
% 206.98/29.45 % (1306621)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=358412660:i=5497:nm=2_2955 on theBenchmark for (2955ds/5497Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306623)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=4065549595:fmbsr=2:i=46332_2955 on theBenchmark for (2955ds/46332Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306627)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=158129815:i=14071_2954 on theBenchmark for (2954ds/14071Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306629)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1940372164:i=22565:add=on:rawr=on_2954 on theBenchmark for (2954ds/22565Mi)
% 206.98/29.45 % (1306567)Instruction limit reached!
% 206.98/29.45 % (1306567)------------------------------
% 206.98/29.45 % (1306567)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306567)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306567)Termination reason: Instruction limit
% 206.98/29.45 % (1306567)Termination phase: Saturation
% 206.98/29.45 % (1306567)Time elapsed: 3.905 s
% 206.98/29.45 % (1306567)Peak memory usage: 19 MB
% 206.98/29.45 % (1306567)Instructions burned: 5132 (million)
% 206.98/29.45 % (1306631)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=1460793824:i=8173:av=off_2953 on theBenchmark for (2953ds/8173Mi)
% 206.98/29.45 % (1306611)Instruction limit reached!
% 206.98/29.45 % (1306611)------------------------------
% 206.98/29.45 % (1306611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306611)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306611)Termination reason: Instruction limit
% 206.98/29.45 % (1306611)Termination phase: Saturation
% 206.98/29.45 % (1306611)Time elapsed: 1.719 s
% 206.98/29.45 % (1306611)Peak memory usage: 20 MB
% 206.98/29.45 % (1306611)Instructions burned: 4593 (million)
% 206.98/29.45 % (1306633)dis+10_16:1_sil=16000:random_seed=913107556:i=9155:fsr=off_2952 on theBenchmark for (2952ds/9155Mi)
% 206.98/29.45 % (1306633)Instruction limit reached!
% 206.98/29.45 % (1306633)------------------------------
% 206.98/29.45 % (1306633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306633)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306633)Termination reason: Instruction limit
% 206.98/29.45 % (1306633)Termination phase: Saturation
% 206.98/29.45 % (1306633)Time elapsed: 3.287 s
% 206.98/29.45 % (1306633)Peak memory usage: 21 MB
% 206.98/29.45 % (1306633)Instructions burned: 9157 (million)
% 206.98/29.45 % (1306643)ott-3_8_sil=64000:random_seed=1083125882:i=20139:bs=on_2919 on theBenchmark for (2919ds/20139Mi)
% 206.98/29.45 % (1306618)Instruction limit reached!
% 206.98/29.45 % (1306618)------------------------------
% 206.98/29.45 % (1306618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306618)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306618)Termination reason: Instruction limit
% 206.98/29.45 % (1306618)Termination phase: Saturation
% 206.98/29.45 % (1306618)Time elapsed: 4.254 s
% 206.98/29.45 % (1306618)Peak memory usage: 24 MB
% 206.98/29.45 % (1306618)Instructions burned: 5211 (million)
% 206.98/29.45 % (1306645)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=1594984749:fmbsr=2:i=32576_2918 on theBenchmark for (2918ds/32576Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306647)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=1511541181:i=11404_2917 on theBenchmark for (2917ds/11404Mi)
% 206.98/29.45 % (1306631)Instruction limit reached!
% 206.98/29.45 % (1306631)------------------------------
% 206.98/29.45 % (1306631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306631)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306631)Termination reason: Instruction limit
% 206.98/29.45 % (1306631)Termination phase: Saturation
% 206.98/29.45 % (1306631)Time elapsed: 6.141 s
% 206.98/29.45 % (1306631)Peak memory usage: 37 MB
% 206.98/29.45 % (1306631)Instructions burned: 8174 (million)
% 206.98/29.45 % (1306658)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=2808061787:i=14134_2891 on theBenchmark for (2891ds/14134Mi)
% 206.98/29.45 % (1306658)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 206.98/29.45 % (1306643)Instruction limit reached!
% 206.98/29.45 % (1306643)------------------------------
% 206.98/29.45 % (1306643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306643)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306643)Termination reason: Instruction limit
% 206.98/29.45 % (1306643)Termination phase: Saturation
% 206.98/29.45 % (1306643)Time elapsed: 7.336 s
% 206.98/29.45 % (1306643)Peak memory usage: 37 MB
% 206.98/29.45 % (1306643)Instructions burned: 20144 (million)
% 206.98/29.45 % (1306663)dis+33_16_sil=32000:sac=on:random_seed=719527021:i=15851:nm=0_2845 on theBenchmark for (2845ds/15851Mi)
% 206.98/29.45 % (1306647)Instruction limit reached!
% 206.98/29.45 % (1306647)------------------------------
% 206.98/29.45 % (1306647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306647)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306647)Termination reason: Instruction limit
% 206.98/29.45 % (1306647)Termination phase: Saturation
% 206.98/29.45 % (1306647)Time elapsed: 8.288 s
% 206.98/29.45 % (1306647)Peak memory usage: 44 MB
% 206.98/29.45 % (1306647)Instructions burned: 11405 (million)
% 206.98/29.45 % (1306668)dis+4_1024_sil=32000:avsql=on:sp=occurrence:gs=on:avsqc=1:random_seed=3988754664:avsq=on:i=17627:add=on:amm=off_2834 on theBenchmark for (2834ds/17627Mi)
% 206.98/29.45 % (1306629)Instruction limit reached!
% 206.98/29.45 % (1306629)------------------------------
% 206.98/29.45 % (1306629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306629)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306629)Termination reason: Instruction limit
% 206.98/29.45 % (1306629)Termination phase: Saturation
% 206.98/29.45 % (1306629)Time elapsed: 16.186 s
% 206.98/29.45 % (1306629)Peak memory usage: 64 MB
% 206.98/29.45 % (1306629)Instructions burned: 22566 (million)
% 206.98/29.45 % (1306678)ott+10_64_anc=all:sil=128000:sas=cadical:bsr=unit_only:nwc=1:cn=on:random_seed=1418130128:s2a=on:i=53295_2792 on theBenchmark for (2792ds/53295Mi)
% 206.98/29.45 % (1306658)Instruction limit reached!
% 206.98/29.45 % (1306658)------------------------------
% 206.98/29.45 % (1306658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306658)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306658)Termination reason: Instruction limit
% 206.98/29.45 % (1306658)Termination phase: Saturation
% 206.98/29.45 % (1306658)Time elapsed: 10.344 s
% 206.98/29.45 % (1306658)Peak memory usage: 45 MB
% 206.98/29.45 % (1306658)Instructions burned: 14134 (million)
% 206.98/29.45 % (1306680)fmb+10_1_sil=32000:sas=cadical:fmbss=16:random_seed=3458171229:i=26857:ins=20_2787 on theBenchmark for (2787ds/26857Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306682)ott+10_1_sil=64000:plsq=on:plsqc=4:bsr=unit_only:gs=on:random_seed=1786979891:i=28120:bs=on:fsr=off_2787 on theBenchmark for (2787ds/28120Mi)
% 206.98/29.45 % (1306663)Instruction limit reached!
% 206.98/29.45 % (1306663)------------------------------
% 206.98/29.45 % (1306663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306663)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306663)Termination reason: Instruction limit
% 206.98/29.45 % (1306663)Termination phase: Saturation
% 206.98/29.45 % (1306663)Time elapsed: 6.127 s
% 206.98/29.45 % (1306663)Peak memory usage: 24 MB
% 206.98/29.45 % (1306663)Instructions burned: 15854 (million)
% 206.98/29.45 % (1306684)fmb+10_1_sil=256000:fmbss=7:random_seed=2826702782:fmbsr=1.6:i=182295_2784 on theBenchmark for (2784ds/182295Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306686)fmb+10_1_sil=128000:fmbss=21:newcnf=on:random_seed=2478140884:i=44625:gsp=on_2783 on theBenchmark for (2783ds/44625Mi)
% 206.98/29.45 % (1306686)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 206.98/29.45 % (1306686)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306688)fmb+10_1_sil=256000:sas=cadical:fmbss=15:random_seed=2334080673:i=160505_2783 on theBenchmark for (2783ds/160505Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306690)fmb+10_1_sil=256000:tgt=full:fmbss=10:random_seed=2436948924:fmbsr=1.3:i=225729_2783 on theBenchmark for (2783ds/225729Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306692)fmb+10_1_sil=256000:tgt=full:sas=cadical:fmbss=10:random_seed=2109166967:fmbsr=2:i=185024:ins=7_2783 on theBenchmark for (2783ds/185024Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306694)fmb+10_1_sas=cadical:si=on:bce=on:rp=on:random_seed=1998179532:rtra=on_2782 on theBenchmark for (2782ds/0Mi)
% 206.98/29.45 % Exception at run slice level
% 206.98/29.45 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 206.98/29.45 % (1306696)% WARNING: option uhcvi not known.
% 206.98/29.45 % (1306696)dis+11_61:31_drc=ordering:si=on:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2239299329:i=271062:add=off:rtra=on:rawr=on_2782 on theBenchmark for (2782ds/271062Mi)
% 206.98/29.45 % (1306696)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 206.98/29.45 % (1306696)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 206.98/29.45 % (1306613)Instruction limit reached!
% 206.98/29.45 % (1306613)------------------------------
% 206.98/29.45 % (1306613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306613)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306613)Termination reason: Instruction limit
% 206.98/29.45 % (1306613)Termination phase: Saturation
% 206.98/29.45 % (1306613)Time elapsed: 21.364 s
% 206.98/29.45 % (1306613)Peak memory usage: 28 MB
% 206.98/29.45 % (1306613)Instructions burned: 29340 (million)
% 206.98/29.45 % (1306702)dis+10_161_sil=256000:plsq=on:si=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=217462138:i=176048:add=on:rtra=on:rawr=on_2749 on theBenchmark for (2749ds/176048Mi)
% 206.98/29.45 % (1306696) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1306520-1306696"...
% 206.98/29.45 % (1306696)...printing done.
% 206.98/29.45 % (1306696)Refutation found. Thanks to Tanya!
% 206.98/29.45 % SZS status Theorem for theBenchmark
% 206.98/29.45 % SZS output start Proof for theBenchmark
% See solution above
% 206.98/29.45 % (1306696)------------------------------
% 206.98/29.45 % (1306696)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 206.98/29.45 % (1306696)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 206.98/29.45 % (1306696)CaDiCaL version: 2.1.3
% 206.98/29.45 % (1306696)Termination reason: Refutation
% 206.98/29.45 % (1306696)Time elapsed: 7.367 s
% 206.98/29.45 % (1306696)Peak memory usage: 28 MB
% 206.98/29.45 % (1306696)Instructions burned: 21194 (million)
% 206.98/29.45 % (1306520)Success in time 29.128 s
% 206.98/29.45 % Vampire exiting
%------------------------------------------------------------------------------